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Characterization of microroughness parameters in gadoliniumoxide thin films: A study based on extended power

spectral density analyses

M. Senthilkumar, N.K. Sahoo *, S. Thakur, R.B. Tokas

Spectroscopy Division, Bhabha Atomic Research Centre, Modular Laboratories, Trombay, Mumbai 400 085, India

Received 1 December 2004; received in revised form 28 February 2005; accepted 28 February 2005Available online 8 April 2005

Abstract

Spectral microroughness is a performance-limiting factor for optical thin films like Gd2O3, which have dedicative

applications in ultraviolet or deep ultraviolet region of the electromagnetic spectrum. Such a morphological parameter of a

thin film surface can be very well characterized by power spectral density (PSD) functions. The PSD provides a more reliable

description to the topography than the RMS roughness and imparts several useful information of the surface including fractal and

superstructure contributions. Through the present study it has been noticed that deposition parameters like evaporation rate and

oxygen pressure can play very definite, dominant and predictable roles in the evolution of fractal and superstructures in thin film

topographies recorded through atomic force microscopy (AFM). In this work, the PSD functions derived from morphologies of

various gadolinia thinfilms have been fitted with a novel multi peak-shifting Gaussian model along with fractal and k -correlationfunctions, to extract characteristic parameters of the precision surfaces. Using such information, roughness contributions of the

fractal components (substrate dominated), pure film and the aggregates have been successfully extracted. Higher spectral fractal

strengths have depicted lower refractive index values. The microroughness and grain sizes of the pure film have been influenced

very differently with deposition rate and oxygen pressure. The oxygen pressure strongly influenced the grain sizes where as the

deposition rate influenced the microroughness of the gadolinia films.

# 2005 Elsevier B.V. All rights reserved.

PACS: 42.79W; 68.35.C; 61.16C; 81.15E

Keywords: Reactive electron beam evaporation; Surface microroughness; Power spectral density

1. Introduction

Because of the growth in the field of the

semiconductor technology, the optical coating require-

ments in the ultraviolet (UV) and deep ultraviolet

(DUV) region have been facing severe challenges to

www.elsevier.com/locate/apsuscApplied Surface Science 252 (2005) 1608–1619

* Corresponding author. Tel.: +91 22 25593871;

fax: +91 22 25505151.

E-mail address: [email protected] (N.K. Sahoo).

0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2005.02.122

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meet the development criteria [1]. For example, deep

UV photolithography with an ArF excimer laser source

at a wavelength of 193 nm has been identified as a very

attractive candidate for this potential process. The mostpreferable oxide optical coating materials are unsui-

table in this spectral region due to their low band gap

values. Although fluorides have some favourable

transmission properties, because of their poor index

ratiosan excessive high numberof layersare required to

achieve the desired reflectivity in this wavelength

region. Recently it has been demonstrated that electron

beam deposited gadolinia (Gd2O3) films under low

substrate temperatures can be very conveniently used to

193 nm (ArF) spectral region dueto its favourable band

gap values [2,3]. Most notably, the optical coating

performance-limiting factors in this spectral region is

predominantly decided by the quality of the micro-

structureand overall morphology of such thin films. For

a reactively electron beam evaporated gadolinium

oxide thin film at low substrate temperature, deposition

rate and oxygen pressure can have strong influences on

the grain structure as well as morphology evolutions. In

order to design and develop an efficient low scattering

multilayer device, it is essential to explore such

parametric dependence of the surface topography.

In general, the microroughness characterization of

a thin film surface can be carried out using optical or

mechanical profiler or an atomic force microscope

(AFM). However, AFM can be advantageously usedwith high vertical and spatial resolution to extract

microroughness information of the surfaces [4]. Such

roughness information obtained from AFM can be

advantageously employed to the successful develop-

ment of low scatter optical multilayer coatings. In

addition, such information about the surface rough-

ness is extremely useful for the alternate optical

characterization of thin films using ellipsometry or

spectrophotometry.

As mentioned above, gadolinia films deposited at

lower substrate temperature exhibit high band gaps,

which is very useful for developing deep UV opticalcoatings. Hence, in the present study, main thrust has

been given to the films deposited under such substrate

conditions. Several samples of gadolinium oxide films

have been prepared using reactive electron beam

evaporation technique by varying the deposition rate

and oxygen pressure. The surface height profiles of the

films have been measured using atomic force micro-

scopy with different pre-decided scan sizes. The power

spectral density (PSD) functions of all the surface

profiles of each filmhave been computed and combined

in to a single PSD profile covering large spatialfrequency bandwidth. These experimentally derived

PSDs have been fitted with appropriate analytical

models. During our investigation, some of the experi-

mental PSD profiles have exhibited more than one local

maximum at lower spatial frequency region suggesting

the presence of superstructures in the films. Hence, the

existing PSD models have been suitably modified to

account for the superstructures present in such thin

films. From this fitting, the surface characteristic

parameters relating to fractal properties (substrate

dominated), roughness information of pure film and

aggregates have been obtained for all the gadolinia

films. Such information has helped to understand the

influence of deposition conditions on microroughness

introduced by the fractal components, pure film and the

aggregates. In addition, one can advantageously use

such information in tailoring a surface morphology

according to the requirements by choosing appropriate

deposition conditions.

In the present investigation concerning reactive

electron beam deposition, the two process parameters

such as deposition rate and oxygen pressure have been

observed to affect the surface morphology very

differently. The oxygen pressure depicted a stronger

influence on surface lateral features (grain size) of purefilms than the rate of evaporation. On the other hand,

deposition rate has shown a stronger influence on RMS

roughness of gadolinia films than the oxygen pressure.

The deposition rate has also demonstrated a stronger

influence on fractal nature of the films than the oxygen

pressure. Besides, the higher values of fractal strengths

have been observed to be associated with lower refrac-

tive indices. Aggregates have been invariably found in

all the films deposited at low substrate temperature

conditions.However,themicroroughnessofthefilmdue

to aggregates increases with the increase in oxygen

pressure.Thedetailsofthesurfacetopographicstudyarepresented in the subsequent sections.

2. Microroughness characterization

As mentioned earlier, the microroughness or

morphology of an optical surface is most popularly

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characterized by the power spectral density (PSD)

functions. PSD functions describe two aspects of the

surface roughness such as the spread of heights from

a mean plane, and the lateral distance over which theheight variation occurs [5]. Hence, PSD explains a

surface much better than the RMS roughness and

provides very useful information on fractals and

superstructures that may coexist in the microstruc-

tures. It has been realized recently that the fractal

geometry and scaling concepts can concisely

describe the rough surface morphology [6,7]. The

surface morphology at different scales is believed

to be self-similar and related in the fractal geometry.

The ability of fractal analyses to extract many

different types of information from measured

textures compared to common, conventional ana-

lyses makes this approach very useful in describing

surface characteristics of thin films. Several studies

have demonstrated that the complexity of thin film

morphology were fractal in nature, and can be

characterized quantitatively by the fractal strengths

and their dimensions as well [6,7]. Such an analysis

employing the PSD information over a large spatial

frequency scale has been applied to the present

gadolinium oxide thin film surfaces. The following

section puts some light on the PSD and its analysis

techniques.

2.1. Thin films and power spectral density functions

The power spectral density function of thin films

can be derived from the measurements of the bi-

directional reflectance distribution function (BRDF)

or from surface profiles measured by an optical or

mechanical profiler or from the AFM surface profile

data [5]. Amongst these techniques, AFM is an

excellent tool for characterizing the surfaces and

widely being used in studying optical thin film

surfaces.

There have been large numbers of publications

dealing with PSD calculations from the surface profiledata. The computation of PSD function adopted in this

paper is given by [8],

S 2ð f x; f yÞ ¼1

L 2

X N m¼1

X N n¼1

Z mn eÀepiD L ð f xmþ f ynÞðD L Þ2

" #2

(1)

where S 2 denotes the two-dimensional PSD, L 2 is the

scanned surface area, N is the number of data points

per line and row, Z mn is the profile height at position

(m, n), f x, f y are the spatial frequency in the x- and y-directions and D L = N / L is the sampling distance.

This computation is further followed by the

transition to polar co-ordinates in frequency space

and angular averaging ({w})

S 2ð f Þ ¼1

2p

Z 2p

0S 2ð f ;’Þ d’ (2)

As the PSD function depends on only one parameter, it

is plotted in all our figures as a ‘‘slice’’ of the two

dimensional representation. It remains a two dimen-

sional function with a unit of fourth power to the

length, i.e., ‘‘(length)

4

’’.Conventionally, PSD functions obtained from

AFM measurements have roughness values in a limi-

ted range of spatial frequencies. The range depends on

the scan length and sampling distance, and it also can

be additionally restricted or constrained by the effect

of measurements artifacts. These limitations, however,

can be overcome when the topographic measurements

performed on different scales are appropriately

combined, provided it fulfills following two condi-

tions:

(i) The spatial frequency ranges where the measure-

ments are defined should partially overlap. Thecondition is easy to meet by adequate selection of

the scan sizes and the sampling distances.

(ii) In the overlapping region, the different PSD

functions should be the same order of magnitude.

With these criteria, the combined PSD function at a

desired frequency is described by the geometrical a-

verage and it is given by,

PSDcombinedð f Þ ¼

Y N

i¼1

PSDið f Þ

" #1= N

(3)

where N is the number of PSD functions overlapping

at the concern frequency. In the present work, the

measurements have been performed at the same posi-

tion and with three different scan sizes: 0.45 mm Â0.45 mm, 2 mm Â 2 mm and 5 mm Â 5 mm. The PSD

functions have been computed separately for each

scan. The values so obtained have been suitably

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combined and averaged in order to obtain PSD for the

desired extended spatial frequency range. To interpret

an experimental PSD function an appropriate analy-

tical model is highly essential which provide deepinsight to the microscopic parametric dependence.

Next section highlights this aspect of model based

PSD interpretation.

2.2. PSD models for the microroughness

interpretation

As described earlier, the PSD contains a more

complete description than the RMS roughness and

provides useful quantitative information of a thin film

surface morphology. However, appropriate analytical

models aid to the interpretation and understanding of

such morphologies more qualitatively. In the past,

several such models have been used to describe

specific optical surfaces and thin films. These models

consist of a function or combination of functions

approximating the experimental PSD functional

behavior. The most favourable extended model for

the PSD of a thin film coating uses the sum of Henkel

transforms of Gaussian and exponential autocorrela-

tion function [9–11]. This model has been extensively

used and led to satisfactory results in some specific

cases. However, such an approach has a deficiency

when wide-range of spatial frequencies is considered.

In general, PSD of a thin film coating can beapproximated to a sum of PSD of the substrate and the

PSD of the pure film [12]. Moreover, in order to

describe the surface roughness over large range of

spatial frequencies, the PSD analytical model should

include the mathematical term describing the overall

roughness contribution from the substrate (fractals),

pure film and aggregates. PSD of the substrates with

spatial frequencies ( f ) mostly follows a fractal model,

which obeys the inverse power law [13], i.e.,

PSDfractalð f ;K ; nÞ ¼K

f nþ1(4)

The intrinsic surface parameters describing such frac-

tal-like surfaces are spectral strength (K ) and spectral

indices (n) rather than RMS roughness (s ) and corre-

lation length (l). This PSD form is obtained when it is

assumed that the surface is self-affine, which is the

case with varieties of precision substrates. The fractal

dimension, ‘‘ D’’ which some times mentioned by

various experimentalists during the PSD analyses, is

given by,

D ¼ 12ð5 À ðn þ 1ÞÞ ¼ 1

2ð4 À nÞ; with 0< n< 2

(5)

The dimension parameter has several meanings. For

instance, the case D = 2 (n = 0) is called the extreme

fractal; D = 1.5 (n = 1) the Brownian fractal; and

D = 1 (n = 2) the marginal fractal.

Apart from substrate’s fractal characteristics,

sometimes, thin film coatings tend to develop fractal

nature during the growth stages. The power spectra of

most of our experimental PSD profiles of gadolinium

oxide films exhibit similar characteristics especially at

high spatial frequency regions, which indicate the

presence of strong fractal components in the thin filmtopographies. It is, therefore, essential to include an

appropriate fractal model to extract roughness con-

tribution of fractal components from the total rough-

ness of such thin films.

Morphological parameters and their analyses for

the coated and uncoated substrates need different as

well as appropriate insight to the characterization task.

Fortunately, the function for describing the PSD of the

pure film can be conveniently made use of the k -

correlation model (also called as ABC model), which

is given by [14,15],

PSDABC ¼

A

ð1 þ B2 f 2ÞðC þ1Þ=2 (6)

with A, B, C being parameters. This model satisfacto-

rily describes random rough surfaces over large length

scales. Eq. (6) gives a PSD function with a ‘‘knee,’’

determined by B, which is equal to the correlation

length. At small f values, well below the knee or the

crossover region, the PSD is determined by A, and at

high f values, beyond the knee, the surface is fractal

and the PSD function is determined by C. However,

the equivalent RMS roughness s ABC and correlation

length t ABC that depend on these three parameters can

be derived as follows:

s 2ABC ¼

2p A

B2ðC À 1Þ; t

2ABC ¼

ðC À 1Þ2 B2

2p2C (7)

All the above models are monotonically decreasing

functions of spatial frequency and cannot account for

any additional morphological features. However, it

has been observed that several experimental thin films


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show the formation of superstructures uniformly dis-

tributed along the surface. This induces a local max-

imum in the lower frequencies of the PSD that cannot

be explained by any of such previous models. Model-ing of such local maxima in PSDs can be carried out

using a Gaussian function with its peak-maximum

shifted to a non-zero spatial frequency as follows [16]:

PSDShð f ; s sh; t sh; f shÞ¼ps 2sht 2shexp½Àp2t 2shð f À f shÞ2

(8)

This PSD corresponds to an autocovariance function

with the form of a Gaussian multiplied by a cosine.

The period of the cosine corresponds to the periodicity

of the superstructures in the surface. The period is

translated into the spatial frequency domain as the

shift of the PSD maximum to the frequency f sh. Themeaning of the other model parameters can also be

related to the various other characteristics of these

superstructures. For example here, t sh corresponds to

the size and s sh to the height of the superstructures.

In order to describe the PSD over a large spatial

frequencybandwidth, Ferre-Borrull et al. [8], haveused

a model that includes above three Eqs. (4), (6) and (8).

With this PSD model, they have satisfactorily

characterized the surface topographies of ion beam

sputtered MgF2 thin filmcoatings. ThePSD modelused

by themdescribes the experimentalPSD behaviorwhen

there is only one local maximum in the profile.

However, the most evaporated films like ours often

exhibit superstructures having different values s sh and

t sh distributed over the film surfaces. For such films,

PSD exhibits more than one local maximum, which

cannot be described using the above formalism.

However, by adopting a combination of shifted

Gaussian functions along with fractal and k -correlation

functions it is possible to explain the presence of

multiple local maxima. In the present investigation,

such a multi peak-shifting Gaussian model approach

has been employed, which is given by,

PSDtotal ¼

K

f nþ1 þ

A

ð1 þ B2 f 2ÞðC þ1Þ=2

þXm

ps 2sh;mt 2sh;m exp½Àp2t 2sh;mð f À f sh;mÞ2

(9)

The experimental PSD curves of our gadolinia films

have been fitted with this modified analytical model.

As an example of this analysis method, experimental

PSD of the films deposited at two different parametric

conditions and their fitting results are presented in

Fig. 1. The fractal roughness components of substrate,intrinsic film roughness and superstructures have been

derived from this modeling. In Fig. 1(a) a local max-

imum at spatial frequency of 0.183 mmÀ1 is exhibited

in the experimental PSD curve. However, in Fig. 1(b),

two local maxima have been exhibited at 0.185

and 1.1 mmÀ1. The goodness of the fit justifies the

use of present analytical model for our evaporated

films.

3. Experimental details

3.1. Sample preparation

Several thin film samples of Gd2O3 films have been

deposited on quartz substrate using reactive electron

beam evaporation techniques with the optical thick-

ness of 8l /4 (at l = 600 nm). Optical thickness of the

films has been monitored using Leybold’s OMS-2000

optical monitor. The deposition rate of evaporation has

been controlled using Inficon’s XTC/2 quartz crystal

monitor. During the deposition, the evaporation rate

has beenvaried from5 to 20 A´ /s. However, the oxygen

pressure has been varied from 0.5 Â 10À4 to

2.0 Â 10À4

mbar. Most of the films in the presentstudy were deposited at the substrate temperature of

70 8C. This is because this film material, according to

our earlier studies, has been observed to yield high

optical band gap values (>6 eV) at such low and

ambient substrate temperature deposition conditions.

This happens to be a very useful as well as favourable

property in making thin film optical multilayer devices

for deep UV optical applications [2,3]. All the films

have been subsequently characterized for surface

topography using atomic force microscope.

3.2. Atomic force microscopy characterization

The surface topographic measurements have been

carried out using NT-MDT’s solver-P47H ambient

based multimode atomic force microscope. The

contact mode of AFM has been chosen for the

topographic measurements. A silicon cantilever

having typical radius of curvature of 10 nm, force


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constant of 0.1 N/m and apex angle of 228 has been

used for the measurements. Scans have been made

over areas of 0.5mm Â 0.5 mm, 2 mm Â 2 mm and

5 mm Â 5 mm with the resolution of 256 pix-els Â 256 pixels for each film. Subsequently, the

PSD functions have been calculated according to

Eqs. (1) and (2) for all scan areas. By combining all the

PSD functions according to Eq. (3), a PSD over a large

spatial frequency bandwidth has been obtained. This

procedure has been adopted for all the films deposited

at different deposition conditions.

4. Results and discussions

The experimental PSD functions computed for the

gadolinia films have been fitted with the analyticalmodel described in Eq. (9). The least square

minimization method has been employed to fit all

the experimental PSD curves. The fitting parameters

obtained from this procedure are presented in Table 1.

In the present investigation, our prime objective is to

study the surface topography of gadolinia films

deposited at low ambient substrate temperature

conditions. For a comparative study, a few films have

also been deposited at elevated substrate temperature

also. Such a comparison also highlights the impor-

tance and choice of lower substrate temperature values

for the present gadolinia films.

4.1. Influence of the substrate temperature on

microroughness

The topographies of the films deposited under

elevated temperature conditions have shown distinct

morphological changes. Such a measurement result

has been compared here with the topographies of films

deposited at low ambient conditions. Fig. 2 presents,

the typical topographies of films deposited at the

substrate temperatures of 70 and 250 8C respectively.

During the deposition of these films, the oxygen

pressure and deposition rate have been kept at0.8 Â 10À4 mbar and 10 A /s respectively. In this

figure, the topography of the film deposited at high

substrate temperature depicts the presence of grain of

similar sizes over the surface. In addition, they are

distributed densely over the substrate. However,

topography of the film deposited at low substrate

temperature depicts the grains of different sizes, which

are distributed over the surface. In addition, film

deposited at elevated temperature has formed rela-

tively larger grain sizes compared to the film deposited

at lower substrate temperature. This observation can

be attributed to the influence of surface mobility of theadatoms in the nucleation stages of the film growth.

More qualitative information has been obtained from

the PSD function of these surfaces and their

characteristic parameters. The PSD functions com-

puted for these films are presented in Fig. 3. It can be

seen from this figure that the PSD function of the film

deposited at the high substrate temperature shows


Fig. 1. Fitting of experimental PSD curves of gadolinium oxide

films using an analytical model that consists of (a) one shifted

Gaussian and (b) two shifted Gaussian, along with the fractal and

ABC functions.

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slower variation over the spatial frequency suggesting

the larger lateral structures (grain size) present in this

film than the PSD of the film deposited at low substrate

temperature. In addition, mid and high spatial

frequency regions depicts larger spectral roughness

for the film deposited at elevated substrate tempera-

ture. The characteristic parameter extracted for these

samples (sample nos. 2 and 9) are presented in Table 1.

The intrinsic roughness parameters s ABC and t ABCcalculated using Eq. (7) from the characteristic

parameters for the film deposited at high substrate

temperature are 0.69 and 54.85 nm respectively.Where as the values of s ABC and t ABC for the film

deposited at low ambient substrate temperature are

0.33 and 45.49 nm respectively. It can be visualized

from the PSD analysis that the film deposited at low

substrate temperature yields lower intrinsic film

roughness and lateral features compared to films

deposited at high substrate temperatures.

In order to make complete understanding about the

surface topographies of these films, it is necessary to

analyze the remaining fractal components and

aggregates (shifted Gaussian parameters) of the film.

The PSDs of both the films exhibit inverse power lawvariation especially at the high spatial frequency

region suggesting the presence of fractal components

in the surface topographies. The spectral indices (n)

for the both the films are almost same (see Table 1).

This is also evident from the high frequency regions of

the PSD curve where the slopes of the PSD curve are

same. However, the spectral strength (K ) is higher in

the case of the film deposited at high substrate

temperature. This analysis concludes that the film

deposited at higher substrate temperature appears to

have stronger fractal components than the low

temperature films.

It is well known that the low frequency components

of the PSD spectrum represent the aggregates. The

presence of such aggregates can be seen from the PSD

spectra of these films. The low temperature films

depicted higher spectral roughness at lower spatial

frequency regions suggesting that aggregates have

dominantly contributed to the roughness. Thisobservation is a contrast to the film deposited at

higher substrate temperatures. However, the intrinsic

roughness of the film deposited at low substrate

temperatures is low. Similar analyses have been

carried out for such films deposited at different

deposition rate and oxygen pressure. The details of the

characterization of these films are presented in the

following sections.

4.2. Influence of oxygen pressure

The oxygen pressure during the deposition not onlycontrols the stoichiometry of the films but also

influences the surface properties to a great extent.

Fig. 4 depicts the PSD profiles of gadolinia films

deposited at different oxygen pressure. It can be

observed from this figure that the high spatial

frequency regions for all films obey the inverse power

law variation indicating a presence of strong fractal


Table 1

Fitting coefficients of PSD spectra of Gd2O3 films deposited at different process conditions

Sample

number

Deposition conditions Fractal k -correlation Shifted Gaussian

Rate(A /s)

O2 pressure(Â10À4 mbar)

Substratetemperature

(8C)

K (10À3 nm)

n A(102 nm)

B(nm)

C Term-1 Term-2s 1

(nm)

t 1

(nm)

x1(mmÀ1)

s 2

(nm)

t 2

(nm)

x2(mmÀ1)

1 5 0.8 70 1.9 1.0 14.5 125 4.6 0.6 320 0.65 – – –

2 10 0.8 70 1.3 1.02 92.0 95 7 0.5 150 0.3 0.23 510 0.4

3 15 0.8 70 6.0 1.00 160.0 230 5 0.4 10 2.055 – – –

4 20 0.8 70 8.13 1.05 265.0 225 7 0.39 400 0.35 – – –

5 10 0.5 70 0.31 1.05 75.5 130 12 0.21 980 1.1 0.7 800 0.185

6 10 0.8 70 1.3 1.02 92.0 95 7 0.5 150 0.3 0.23 510 0.4

7 10 1.5 70 1.5 1.05 65.5 130 10 0.78 690 0.183 – – –

8 10 2.0 70 0.5 1.15 105.0 230 5 0.72 450 0.42 – – –

9 10 0.8 250 6 1.0 99.3 330 2.2 0.496 300 0.3 – – –

Some of the films can be seen to fit very well with a single shifted-Gaussian term.

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components in the film topographies. The slopes of the

PSDs in this region are almost same indicating all the

films poses same values of fractal spectral indices (n).

However, the spectral strength (K ) is noticed to vary in

this region. In order to confirm this observation and to

extract the intrinsic roughness of the films, the PSD

profiles have been fitted with the model presented in

Eq. (9). The characteristic parameters obtained from

the fitting procedure are presented in Table 1. The plot

of spectral strength computed for the films deposited

at different oxygen pressure is shown in Fig. 5. It can

be noted from this figure that the spectral strength is

strongly influenced by the oxygen pressure. The

lowest value of spectral strength has obtained for the

film deposited at the oxygen pressure of 0.8 Â10À4 mbar. However, the spectral indices computed


Fig. 2. Surface topography of gadolinium oxide films deposited at

the substrate temperature of (a) 70 8C and (b) 250 8C. Scan area of

these images is 1 mm Â 1 mm.

Fig. 3. The experimental PSD profiles of gadolinium oxide filmsdeposited at 70 and 250 8C respectively.

Fig. 4. The experimental PSD profiles of gadolinium oxide films

deposited at different oxygen pressure. The deposition rate and

substrate temperature during the deposition were fixed at 10 A /s and

70 8C respectively.

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for these films have been varied from 1.02 to 1.15

implying the dominance of Brownian fractals. One of

the noteworthy observations is the correlation between

the fractal strength and the refractive indices of the

sample films. It can be seen from Fig. 6 that the lower

values of the spectral fractal strengths are associated

with the higher refractive indices and vice versa. Such

an observation highlights a strong correlation betweenthe morphology and the microstructure.

The roughness contribution of the pure film has

been extracted using the k -correlation model. The

RMS equivalent roughness (s ABC) and the correlation

length (t ABC) have also been computed from the

characteristic parameter obtained from the fitting

procedure. The plots of s ABC and t ABC with oxygen

pressure are presented in Fig. 7. As it can be seen

from this figure that both the surface characteristic

parameters have been influenced by the oxygen

pressure. Besides, they follow a very similar func-

tional trend. When, high oxygen pressure values havebeen adopted for the deposition, films have exhibited

high values of RMS roughness and correlation length.

However, at optimum oxygen pressure (0.8 Â10À4 mbar), films have demonstrated the lowest

RMS roughness and correlation length. It can also

be observed from this figure that the intrinsic

roughness has varied from 0.33 to 0.56 nm. However,

the correlation length has varied from 45.49 to

97.02 nm. It is, therefore, inferred that oxygen

pressure alter the lateral features of these films more

without causing appreciable changes in the RMS

roughness.

4.3. Influence of the rate of deposition

The rate of evaporation has also influenced the

surface properties of the gadolinia films to a great

extent. Fig. 8 presents the PSD profiles of gadoliniafilms deposited at different rate of evaporation. Both

the high and low spatial frequency regions of the PSD

have been influenced by the deposition rate. However,

the medium frequency region is not very much

affected by this deposition parameter. It is observed

from this figure that the high spatial frequency region

of PSD for all films also obeys the inverse power law

variation indicating the strong presence of fractal

components. Besides, the slope of the PSD in this

region is almost same indicating all the films pose

same values for the fractal spectral indices (n).

However, the spectral strength (K ) observed to vary inthis spectral region. As mentioned earlier, the lower

spatial frequency part of PSD function predominantly

represents the aggregates. It is observed from this

frequency region that aggregates contribute to the total

film roughness to a large extent. In order to get the

complete information about the surfaces, the PSD

profiles were fitted with the model presented in


Fig. 5. The variation of fractal spectral strength (K ) of the filmsdeposited at different oxygen pressure. The deposition rate and

substrate temperature during the deposition were fixed at 10 A /s and

70 8C respectively.

Fig. 6. The variation of refractive indices of the gadolinia films with

fractal strength.

7/27/2019 1-s2.0-S0169433205005763-main


Eq. (9). The characteristic parameter obtained from

the fitting procedure is presented in Table 1. The plot

of spectral strength computed for the films deposited

at different deposition rate is shown in Fig. 9. The

spectral strength (K ) is varied from 1.3 to 8 mm with

rate of evaporation. The lowest value of spectralstrength is obtained for the film deposited at the

deposition rate of 10 A /s. However, the spectral

indices computed for these films vary from 1.0 to 1.05.

It is important to note that the spectral indices (n) for

the films deposited under different oxygen pressure

and deposition rate are almost same. However, the

spectral strength has been more influenced by the

deposition rate than the oxygen pressure. It is therefore

concluded that the deposition rate alters the fractal

property more prominently than the oxygen pressure.

The roughness contribution of the pure film has

also been extracted using the k -correlation model

(ABC model). The RMS equivalent roughness (s ABC)

and the correlation length(t ABC) have also been

computed from the characteristic parameter obtained


Fig. 7. Plots depicting the variation of (a) roughness (s ABC) and (b)

correlation length (t ABC) with different oxygen pressure.

Fig. 8. The experimental PSD profiles of gadolinium oxide filmsdeposited at different rate of evaporation. The oxygen pressure and

substrate temperature during the deposition were fixed at

0.8 Â 10À4 mbar and 70 8C respectively.

Fig. 9. The variation of fractal spectral strength (K ) of the films

deposited at different rate of evaporation. The oxygen pressure and

substrate temperature during the deposition were fixed at

0.8 Â 10À4 mbar and 70 8C respectively.

7/27/2019 1-s2.0-S0169433205005763-main


from Eq. (7). The plots of s ABC and t ABC with the rate

of evaporation are presented in Fig. 10. Both the

parameters shown in this figure have been influenced

by the deposition rate. In addition, both the parameters

follow the same trend with the deposition rate

variation. With our present extreme rate of evapora-

tion, the films have exhibited larger values in RMS

roughness and correlation length. However, atoptimum rate (10 A /s), films yielded lowest RMS

roughness and correlation length. It can also be

observed from this figure that the intrinsic roughness

has been varied from 0.33 to 0.69 nm. However, the

correlation length has been varied from 45.49 to

47.22 nm. It is, therefore, inferred that deposition rate

alters the vertical features (RMS roughness) of the film

appreciably without causing much change in sizes of

the lateral features of the films. This observation is in

contrast to the influence of oxygen pressure on the film

topography.In the present investigation, both deposition rate

and oxygen pressure have influenced the formation of

aggregates. Variation of oxygen pressure has caused

the formation of aggregates with sizes (t sh) ranging

from 150 to 980 nm. Besides, their periodicity has

been varied from 0.183 to 1.1 mmÀ1. Where as the

deposition rate variation has caused the formation of

aggregates or superstructures with sizes (t sh) ranging

from 10 to 500 nm. Their periodicity has been varied

from 0.3 to 2.055 mmÀ1. It can be easily visualized

from this result that oxygen pressure has influenced

the formation of relatively larger size aggregates (t sh)

in the present thin film morphologies. In addition, such

aggregates have been coarsely distributed over the

surface. On the contrary, the deposition rate variation

has influenced the formation of relatively smaller size

aggregates that have been distributed densely over the

film surface.

5. Conclusion

Reactive electron beam evaporated gadolinium

oxide films have exhibited several interesting surface

topographies. The effect of deposition rate and oxygenpressure on surface morphologies has been studied

using detailed power spectral density analyses. The

extended PSD profiles and the interpretation using the

analytical models have yielded several interesting

information about the fractals, intrinsic film roughness

and aggregates of the thin film samples. The rate of

evaporation depicted a strong influence on the

microroughness of the pure film than the grain sizes.

On the other hand, oxygen pressure has portrayed

higher influence on the grain sizes than the micro-

roughness of the pure film. Films deposited under

various rates and oxygen pressure appeared to bemostly of Brownian fractal in nature. The spectral

strength (K ) of the fractal components of the surfaces

has been influenced more by the rate of evaporation

than the oxygen pressure. Both the parameters found

to influence aggregates formation in the thin film

during the growth process. In addition, fractal spectral

strength has been strongly correlated with the


Fig. 10. Plots depictingthe variation of (a)roughness(s ABC) and (b)

correlation length (t ABC) with different rate of evaporation. The

oxygen pressure and substrate temperature during the deposition

were fixed at 0.8 Â 10À4 mbar and 70 8C respectively.

7/27/2019 1-s2.0-S0169433205005763-main


refractive index of the film. In the present study, it has

been inferred that by systematically varying

the process conditions, it is possible to achieve a

relatively smooth morphology with an optimumparametric set. It is evident from our study that the

optimum deposition condition (oxygen pressure =

0.8 Â 10À4 mbar and deposition rate = 10 A /s) yields

this type of smooth and desirable morphology. Such

process optimization is very essential to develop low

scatter optical coatings for UV and deep UV laser

applications.

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